Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptote: ; Horizontal asymptote:
B) Vertical asymptote: ; Horizontal asymptote:
C) Vertical asymptote: ; Horizontal asymptote:
D) Vertical asymptote: ; Horizontal asymptote:

Question

Find the horizontal and vertical asymptotes of the graph of the function. ​  ​
A) Vertical asymptote: ; Horizontal asymptote: 
B) Vertical asymptote: ; Horizontal asymptote: 
C) Vertical asymptote: ; Horizontal asymptote: 
D) Vertical asymptote: ; Horizontal asymptote:

Quizplus · Accepted Answer

To find the horizontal asymptote, we look at the degrees of the numerator and denominator. The degree of the numerator is 2 and the degree of the denominator is 1. Therefore, there is a horizontal asymptote at y = 0 (since the numerator's degree is less than the denominator's).

To find the vertical asymptotes, we set the denominator equal to 0 and solve for x.

x^2 - 4 = 0 
(x+2) (x-2) = 0 
x = -2 or x = 2

Therefore, there are vertical asymptotes at x = -2 and x = 2.

The only choice that matches these asymptotes is C.

Find the Horizontal and Vertical Asymptotes of the Graph of the Function